Construct a confidence interval to estimate the proportion of U.S. adults who ate healthy b)Interpret your confidence c)This is a very precise confidence interval with a very, very small margin of error (0.08% is less than 1/10 of one percent). Why do you think the margin of error is so small for this poll?

In 2014, about 11.3% of U.S. workers belonged to a union. Suppose a sample 400 of U.S. workers is collected to determine whether union efforts to organize have increased union membership. Which if the following is the best description of what u- represents? O A. -is the average sample proportion for all possible samples of size 400 O B. H- is the average number of U.S. workers that belong to a union in all possible samples of size 400 C. O C.H- is the number of all U.S. workers that belong to a union. O D. H- is the proportion of U.S. workers in the sample that belong to a union O E. µ – is the proportion of all U.S. workers that belong to a union

An issue of Time Style and Design reported on a poll conducted on the shopping habits of wealthy Americans. A total of 603 interviews were conducted among a national sample of adults with household incomes of at least $150,000. Of the adults interviewed, 410 said they had purchased clothing, accessories or books online in the past year. We want to understand the percentage of wealthy Americans who shop online. Do the data provide sufficient evidence to say that the majority (more than 50%) of wealthy Americans shop online at the 5% significance level? a. What are n, x, n-x and ??̂? b. State the null and alternative hypotheses. c. What is the value for the test statistic z0? d. Find the p-value. e. Do the data support that (more than 50%) of wealthy Americans shop online?

he North American Free Trade Agreement (NAFTA) enacted in 1994 is a trilateral trade agreement signed by the United States, Canada and Mexico. This trade agreement has been controversial since its inception and Americans remain split on the issue. In a Gallup Poll conducted February 1-5, 2017, 420 out of 912 randomly selected Americans aged 18 or older stated that they believed that NAFTA was bad for the United States. Find the point estimate for the proportion of Americans who believe that NAFTA was bad for the United States. Round your answer to 4 decimal places. Find the margin of error for a 95% confidence interval. Round your answer to 4 decimal places. Construct the 95% confidence interval for the proportion of Americans who believe that NAFTA was bad for the United States. Enter your answer as an open interval of the form (a,b) and round to 3 decimal places. Can you conclude that more than half of Americans believe that NAFTA was bad for the United States? No conclusions can…

Income Tax and the IRS. In 2010, the Internal Revenue Service (IRS) sampled 308,946 tax returns to obtain estimates of various parameters. Data were published in Statistics of Income, Individual Income Tax Returns. According to that document, the mean income tax per return for the returns sampled was $11,266. a. Explain the meaning of sampling error in this context.b. If, in reality, the population mean income tax per return in 2010 was $11,354, how much sampling error was made in estimating that parameter by the sample mean of $11,266?c. If the IRS had sampled 400,000 returns instead of 308,946, would the sampling error necessarily have been smaller? Explain your answer.d. In future surveys, how can the IRS increase the likelihood of small sampling error?

Crime incidents by quarantine violators. On June 10, 2020, CNN Philippines reported that the Philippine National Police (PNP) said that incidents of crime had decreased sharply during the country’s community quarantine, which lasted for 84 days. Concurrently, the Joint Task Force COVID Shield reported that a total of 193,779 quarantine violators had been warned, fined, or arrested. About 65.05% of them were from Luzon. Consider a random sample of 500 quarantine violators. a. Compute m and s for the random variable x, the num- ber of quarantine violators who are from Luzon. b. From the sample of 500 quarantine violators, is it likely that less than half are not from Luzon? Explain.

5. A credit score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Values range from 300 to 850, with a credit score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 702.9. A credit analyst wondered whether high-income individuals (incomes in excess of $100,000 per year) had higher credit scores. He obtained a random sample of 32 high-income individuals and found the sample mean credit score to be 719.1 with a standard deviation of 80.6. Conduct the appropriate test to determine if high-income individuals have higher credit scores at the a = 0.05 level of significance. State the null and alternative hypotheses. Ho: H (1) H: μ (2) (Type integers or decimals. Do not round.) Identify the t-statistic. to = (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. (3) the null…

1. The percentage of 12- to 17-year-olds who reported talking at least once in the past year with their parents about the dangers of drug, tobacco, or alcohol is 60% nationally. A state youth council believes this proportion is higher in their state, where there has been an intense media campaign about this issue. A survey of randomly chosen students from across the state shows 1032 of 1642 students reporting they are having these conversations with their parents. Is there evidence that the percent of students using drugs, tobacco or alcohol in this state is above the national rate?

Dental health issues remain a barrier to attendance, as evidenced by a 2010 Los Angeles School Attendance Review Board (SARB), which lists dental health, along with homelessness, in the top barriers to attendance. The Dental Hygiene program at West Los Angeles College collects data on its clinic patients to help instructors and students better understand their patient population. From July 2017 to December 2019 the program treated 3421 patients. Students were asked to analyze a random sample of 127 patients from that time period and found that 36.4% had severe periodontal disease (infections and inflammation of the gums and bone that surround and support the teeth). Identify the population: Identify the sample: Identify the parameter of interest: Identify the statistic:

Most alpine skiers and snowboarders do not use helmets. Do helmetsreduce the risk of head injuries? A study in Norway compared skiers and snowboarders who suffered head injuries with a control group who were not injured. Of 578 injured subjects, 96 had worn a helmet. Of the 2992 in the control group, 656 wore helmets. Is helmet use less common among skiers and snowboarders who have head injuries?